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Sensor deployment for pipeline leakage detection via optimal boundary control strategies
1.  State Key Laboratory of Industrial Control Technology, Institute of CyberSystems & Control, Zhejiang University, Hangzhou, Zhejiang 310027, China, China, China 
2.  Institute of Operations Research & Cybernetics, Zhejiang University, Hangzhou, Zhejiang 310027, China 
3.  Ningbo Institute of Technology, Zhejiang University, Hangzhou, Zhejiang 310027, China 
References:
[1] 
N. Ahmed and K. Teo, Optimal Control of Distributed Parameter Systems,, North Holland, (1981). 
[2] 
S. Anita, V. Arnautu and V. Capasso, An Introduction to Optimal Control Problems in Life Sciences and Economics,, Modeling and Simulation in Science, (2011). doi: 10.1007/9780817680985. 
[3] 
V. Arnautu and P. Neittaanmaki, Optimal Control from Theory to Computer Programs,, Kluwer Academic, (2003). doi: 10.1007/9789401724883. 
[4] 
P. Barooah, P. Mehta and J. Hespanha, Mistuningbased control design to improve closedloop stability margin of vehicular platoons,, IEEE Transactions on Automatic Control, 54 (2009), 2100. doi: 10.1109/TAC.2009.2026934. 
[5] 
S. Blazic, D. Matko and G. Geiger, Simple model of a multibatch driven pipeline,, Mathematics and Computers in Simulation, 64 (2004), 617. doi: 10.1016/j.matcom.2003.11.013. 
[6] 
F. Bullo, J. Cortes and S. Martinez, Distributed Control of Robotic Networks (In Applied Mathematics Series),, Princeton University Press, (2009). 
[7] 
M. Chen and D. Georges, Nonlinear optimal control of an openchannel hydraulic system based on an infinitedimensional model,, in Proceeding of the Conference on Decision and Control, (1999). 
[8] 
H. Cho and G. Hwang, Optimal design for dynamic spectrum access in cognitive radio networks under rayleigh fading,, Journal of Industrial and Management Optimization, 8 (2012), 821. doi: 10.3934/jimo.2012.8.821. 
[9] 
E. Chow, L. Hendrix, M. Herberg, S. Itoh, B. Kong, M. Lall and P. Srevens, Pipeline Politics in Asia: The Intersection of Demand, Energy Markets, and Supply Routes,, National Bureau of Asian Research, (2010). 
[10] 
Y. Ding and S. Wang, Optimal control of openchannel flow using adjoint sensitivity analysis,, Journal of Hydraulic EngineeringASCE, 132 (2006), 1215. doi: 10.1061/(ASCE)07339429(2006)132:11(1215). 
[11] 
Z. Feng, K. Teo and V. Rehbock, Branch and bound method for sensor scheduling in discrete time,, Journal of Industrial and Management Optimization, 1 (2005), 499. doi: 10.3934/jimo.2005.1.499. 
[12] 
Z. Feng, K. Teo and V. Rehbock, Hybrid method for a general optimal sensor scheduling problem in discrete time,, Automatica, 44 (2008), 1295. doi: 10.1016/j.automatica.2007.09.024. 
[13] 
G. FerrariTrecate, A. Buffa and M. Gati, Analysis of coordination in multiagent systems through partial difference equations,, IEEE Transactions on Automatic Control, 51 (2006), 1058. doi: 10.1109/TAC.2006.876805. 
[14] 
P. Frihauf and M. Krstic, Leaderenabled deployment onto planar curves: A pdebased approach,, IEEE Transactions on Automatic Control, 56 (2011), 1791. doi: 10.1109/TAC.2010.2092210. 
[15] 
R. Glowinski, J. Lions and J. He, Exact and Approximate Controllability for Distributed Parameter Systems: A Numerical Approach,, (Encyclopedia of Mathematics and its Applications) Cambridge University Press, (2008). doi: 10.1017/CBO9780511721595. 
[16] 
H. Hao and P. Barooah, On achieving sizeindependent stability margin of vehicular lattice formations with distributed control,, IEEE Transactions on Automatic Control, 57 (2012), 2688. doi: 10.1109/TAC.2012.2191179. 
[17] 
H. Hao, P. Barooah and P. Mehta, Stability margin scaling laws for distributed formation control as a function of network structure,, IEEE Transactions on Automatic Control, 56 (2011), 923. doi: 10.1109/TAC.2010.2103416. 
[18] 
J. Kim, K. Kim, V. Natarajan, S. Kelly and J. Bentsman, PdEbased model reference adaptive control of uncertain heterogeneous multiagent networks,, Nonlinear Analysis: Hybrid Systems, 2 (2008), 1152. doi: 10.1016/j.nahs.2008.09.008. 
[19] 
J. Kim, V. Natarajan, S. Kelly and J. Bentsman, Disturbance rejection in robust PdEbased MRAC laws for uncertain heterogeneous multiagent networks under boundary reference,, Nonlinear Analysis: Hybrid Systems, 4 (2010), 484. doi: 10.1016/j.nahs.2009.11.005. 
[20] 
M. Krstic and A. Smyshlyaev, Boundary Control of PDEs: A Course on Backstepping Designs,, SIAM, (2008). doi: 10.1137/1.9780898718607. 
[21] 
Z. Lin, Distributed Control and Analysis of Coupled Cell Systems,, VDM Verlag, (2008). 
[22] 
W. Litvinov, Optimal control of electrorheological clutch described by nonlinear parabolic equation with nonlocal boundary conditions,, Journal of Industrial and Management Optimization, 7 (2011), 291. doi: 10.3934/jimo.2011.7.291. 
[23] 
M. Liu, S. Zang and D. Zhou, Fast leak detection and location of gas pipelines based on an adaptive particle filter,, International Journal of Applied Mathematics and Computer Science, 15 (). 
[24] 
M. Mesbahi and M. Egerstedt, Graph Theoretic Methods in Multiagent Networks (In Applied Mathematics Series),, Princeton University Press, (2010). 
[25] 
T. Meurer and M. Krstic, Finitetime multiagent deployment: A nonlinear pde motion planning approach,, Automatica, 47 (2011), 2534. doi: 10.1016/j.automatica.2011.08.045. 
[26] 
S. Moura and H. Fathy, Optimal boundary control & estimation of diffusionreaction PDEs,, in Proceeding of the Conference on Decision and Control, (2011), 921. 
[27] 
R. Murray, Recent research in cooperative control of multivehicle systems,, Journal of Dynamical Systems, (): 571. 
[28] 
R. OlfatiSaber and R. Murray, Consensus problems in networks of agents with switching topology and timedelays,, IEEE Transactions on Automatic Control, 49 (2004), 1520. doi: 10.1109/TAC.2004.834113. 
[29] 
P. Parfomak, Pipeline Safety and Security: Federal Programs,, Congress Research Services (CRS) Report for Congress, (2008). 
[30] 
M. Rafiee, Q. Wu and A. Bayen, Kalman filter based estimation of flow states in open channels using Lagrangian sensing,, Proceedings of the Conference on Decision and Control, (2009), 8266. doi: 10.1109/CDC.2009.5400661. 
[31] 
W. Ren and Y. Cao, Distributed Coordination of Multiagent Networks,, (Communications and Control Engineering Series) SpringerVerlag, (2011). 
[32] 
A. Sarlette and R. Sepulchre, A PDE viewpoint on basic properties of coordination algorithms with symmetries,, in Proceedings of the Conference on Decision and Control, (2009), 5139. doi: 10.1109/CDC.2009.5400570. 
[33] 
J. Strikwerda, Finite Difference Schemes and Partial Differential Equations, 2nd Edition,, SIAM, (2004). doi: 10.1137/1.9780898717938. 
[34] 
F. Tröltzsch, Optimal Control of Partial Differential Equations: Theory, Methods and Applications (Graduate Studies in Mathematics),, American Mathematical Society, (2010). 
[35] 
G. Wang and H. Ye, Leakage Detection and Localization of Long Distance Fluid Pipelines,, Tsinghua University Press, (2010). 
[36] 
Z. Wang, H. Zhang, J. Feng and S. Lun, Present situation and prospect on leak detection and localization techniques for long distance fluid transport pipeline,, Control and Instruments in Chemical Industry, 30 (2003), 5. 
[37] 
S. Woon, V. Rehbock and R. Loxton, Global optimization method for continuoustime sensor scheduling,, Nonlinear Dynamics and Systems Theory, 10 (2010), 175. 
[38] 
S. Woon, V. Rehbock and R. Loxton, Towards global solutions of optimal discretevalued control problems,, Optimal Control Applications and Methods, 33 (2012), 576. doi: 10.1002/oca.1015. 
[39] 
K. Yiu, K. Mak and K. Teo, Airfoil design via optimal control theory,, Journal of Industrial and Management Optimization, 1 (2005), 133. doi: 10.3934/jimo.2005.1.133. 
[40] 
C. Yu, B. Li, R. Loxton and K. Teo, Optimal discretevalued control computation,, Journal of Global Optimization, 56 (2013), 503. doi: 10.1007/s1089801298587. 
show all references
References:
[1] 
N. Ahmed and K. Teo, Optimal Control of Distributed Parameter Systems,, North Holland, (1981). 
[2] 
S. Anita, V. Arnautu and V. Capasso, An Introduction to Optimal Control Problems in Life Sciences and Economics,, Modeling and Simulation in Science, (2011). doi: 10.1007/9780817680985. 
[3] 
V. Arnautu and P. Neittaanmaki, Optimal Control from Theory to Computer Programs,, Kluwer Academic, (2003). doi: 10.1007/9789401724883. 
[4] 
P. Barooah, P. Mehta and J. Hespanha, Mistuningbased control design to improve closedloop stability margin of vehicular platoons,, IEEE Transactions on Automatic Control, 54 (2009), 2100. doi: 10.1109/TAC.2009.2026934. 
[5] 
S. Blazic, D. Matko and G. Geiger, Simple model of a multibatch driven pipeline,, Mathematics and Computers in Simulation, 64 (2004), 617. doi: 10.1016/j.matcom.2003.11.013. 
[6] 
F. Bullo, J. Cortes and S. Martinez, Distributed Control of Robotic Networks (In Applied Mathematics Series),, Princeton University Press, (2009). 
[7] 
M. Chen and D. Georges, Nonlinear optimal control of an openchannel hydraulic system based on an infinitedimensional model,, in Proceeding of the Conference on Decision and Control, (1999). 
[8] 
H. Cho and G. Hwang, Optimal design for dynamic spectrum access in cognitive radio networks under rayleigh fading,, Journal of Industrial and Management Optimization, 8 (2012), 821. doi: 10.3934/jimo.2012.8.821. 
[9] 
E. Chow, L. Hendrix, M. Herberg, S. Itoh, B. Kong, M. Lall and P. Srevens, Pipeline Politics in Asia: The Intersection of Demand, Energy Markets, and Supply Routes,, National Bureau of Asian Research, (2010). 
[10] 
Y. Ding and S. Wang, Optimal control of openchannel flow using adjoint sensitivity analysis,, Journal of Hydraulic EngineeringASCE, 132 (2006), 1215. doi: 10.1061/(ASCE)07339429(2006)132:11(1215). 
[11] 
Z. Feng, K. Teo and V. Rehbock, Branch and bound method for sensor scheduling in discrete time,, Journal of Industrial and Management Optimization, 1 (2005), 499. doi: 10.3934/jimo.2005.1.499. 
[12] 
Z. Feng, K. Teo and V. Rehbock, Hybrid method for a general optimal sensor scheduling problem in discrete time,, Automatica, 44 (2008), 1295. doi: 10.1016/j.automatica.2007.09.024. 
[13] 
G. FerrariTrecate, A. Buffa and M. Gati, Analysis of coordination in multiagent systems through partial difference equations,, IEEE Transactions on Automatic Control, 51 (2006), 1058. doi: 10.1109/TAC.2006.876805. 
[14] 
P. Frihauf and M. Krstic, Leaderenabled deployment onto planar curves: A pdebased approach,, IEEE Transactions on Automatic Control, 56 (2011), 1791. doi: 10.1109/TAC.2010.2092210. 
[15] 
R. Glowinski, J. Lions and J. He, Exact and Approximate Controllability for Distributed Parameter Systems: A Numerical Approach,, (Encyclopedia of Mathematics and its Applications) Cambridge University Press, (2008). doi: 10.1017/CBO9780511721595. 
[16] 
H. Hao and P. Barooah, On achieving sizeindependent stability margin of vehicular lattice formations with distributed control,, IEEE Transactions on Automatic Control, 57 (2012), 2688. doi: 10.1109/TAC.2012.2191179. 
[17] 
H. Hao, P. Barooah and P. Mehta, Stability margin scaling laws for distributed formation control as a function of network structure,, IEEE Transactions on Automatic Control, 56 (2011), 923. doi: 10.1109/TAC.2010.2103416. 
[18] 
J. Kim, K. Kim, V. Natarajan, S. Kelly and J. Bentsman, PdEbased model reference adaptive control of uncertain heterogeneous multiagent networks,, Nonlinear Analysis: Hybrid Systems, 2 (2008), 1152. doi: 10.1016/j.nahs.2008.09.008. 
[19] 
J. Kim, V. Natarajan, S. Kelly and J. Bentsman, Disturbance rejection in robust PdEbased MRAC laws for uncertain heterogeneous multiagent networks under boundary reference,, Nonlinear Analysis: Hybrid Systems, 4 (2010), 484. doi: 10.1016/j.nahs.2009.11.005. 
[20] 
M. Krstic and A. Smyshlyaev, Boundary Control of PDEs: A Course on Backstepping Designs,, SIAM, (2008). doi: 10.1137/1.9780898718607. 
[21] 
Z. Lin, Distributed Control and Analysis of Coupled Cell Systems,, VDM Verlag, (2008). 
[22] 
W. Litvinov, Optimal control of electrorheological clutch described by nonlinear parabolic equation with nonlocal boundary conditions,, Journal of Industrial and Management Optimization, 7 (2011), 291. doi: 10.3934/jimo.2011.7.291. 
[23] 
M. Liu, S. Zang and D. Zhou, Fast leak detection and location of gas pipelines based on an adaptive particle filter,, International Journal of Applied Mathematics and Computer Science, 15 (). 
[24] 
M. Mesbahi and M. Egerstedt, Graph Theoretic Methods in Multiagent Networks (In Applied Mathematics Series),, Princeton University Press, (2010). 
[25] 
T. Meurer and M. Krstic, Finitetime multiagent deployment: A nonlinear pde motion planning approach,, Automatica, 47 (2011), 2534. doi: 10.1016/j.automatica.2011.08.045. 
[26] 
S. Moura and H. Fathy, Optimal boundary control & estimation of diffusionreaction PDEs,, in Proceeding of the Conference on Decision and Control, (2011), 921. 
[27] 
R. Murray, Recent research in cooperative control of multivehicle systems,, Journal of Dynamical Systems, (): 571. 
[28] 
R. OlfatiSaber and R. Murray, Consensus problems in networks of agents with switching topology and timedelays,, IEEE Transactions on Automatic Control, 49 (2004), 1520. doi: 10.1109/TAC.2004.834113. 
[29] 
P. Parfomak, Pipeline Safety and Security: Federal Programs,, Congress Research Services (CRS) Report for Congress, (2008). 
[30] 
M. Rafiee, Q. Wu and A. Bayen, Kalman filter based estimation of flow states in open channels using Lagrangian sensing,, Proceedings of the Conference on Decision and Control, (2009), 8266. doi: 10.1109/CDC.2009.5400661. 
[31] 
W. Ren and Y. Cao, Distributed Coordination of Multiagent Networks,, (Communications and Control Engineering Series) SpringerVerlag, (2011). 
[32] 
A. Sarlette and R. Sepulchre, A PDE viewpoint on basic properties of coordination algorithms with symmetries,, in Proceedings of the Conference on Decision and Control, (2009), 5139. doi: 10.1109/CDC.2009.5400570. 
[33] 
J. Strikwerda, Finite Difference Schemes and Partial Differential Equations, 2nd Edition,, SIAM, (2004). doi: 10.1137/1.9780898717938. 
[34] 
F. Tröltzsch, Optimal Control of Partial Differential Equations: Theory, Methods and Applications (Graduate Studies in Mathematics),, American Mathematical Society, (2010). 
[35] 
G. Wang and H. Ye, Leakage Detection and Localization of Long Distance Fluid Pipelines,, Tsinghua University Press, (2010). 
[36] 
Z. Wang, H. Zhang, J. Feng and S. Lun, Present situation and prospect on leak detection and localization techniques for long distance fluid transport pipeline,, Control and Instruments in Chemical Industry, 30 (2003), 5. 
[37] 
S. Woon, V. Rehbock and R. Loxton, Global optimization method for continuoustime sensor scheduling,, Nonlinear Dynamics and Systems Theory, 10 (2010), 175. 
[38] 
S. Woon, V. Rehbock and R. Loxton, Towards global solutions of optimal discretevalued control problems,, Optimal Control Applications and Methods, 33 (2012), 576. doi: 10.1002/oca.1015. 
[39] 
K. Yiu, K. Mak and K. Teo, Airfoil design via optimal control theory,, Journal of Industrial and Management Optimization, 1 (2005), 133. doi: 10.3934/jimo.2005.1.133. 
[40] 
C. Yu, B. Li, R. Loxton and K. Teo, Optimal discretevalued control computation,, Journal of Global Optimization, 56 (2013), 503. doi: 10.1007/s1089801298587. 
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